English

Remarks on almost Riemann solitons with gradient or torse-forming vector field

Differential Geometry 2025-08-04 v4

Abstract

We consider almost Riemann solitons (V,λ)(V,\lambda) in a Riemannian manifold and underline their relation to almost Ricci solitons. When VV is of gradient type, using Bochner formula, we explicitly express the function λ\lambda by means of the gradient vector field VV and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature.

Keywords

Cite

@article{arxiv.2008.06413,
  title  = {Remarks on almost Riemann solitons with gradient or torse-forming vector field},
  author = {Adara M. Blaga},
  journal= {arXiv preprint arXiv:2008.06413},
  year   = {2025}
}